Networks, not trees, identify "weak spots" in phylogenetic trees

A major application of networks in exploratory data analysis is to identify signal oddities and visualise ambiguity. Thus, they would be the natural choice when it comes to pinpointing weaknesses in phylogenetic trees. This is particularly so when the aim is to propose a relatively stable (and intuitive) ‘phylogenetic’ (identifying likely monophyla sensu Hennig) or ‘cladistic’ (clade-based) systematic framework for a group of organsims. In other words, whenever we try to translate branching patterns into monophyletic groups.

‘Weak spots’ in phylogenetic trees are relationships with either little or ambiguous support, or branching patterns strongly affected by sampling (taxa and characters). These are topological phenomena that are rather the rule than the exception when studying extinct groups of organisms (e.g. spermatophytes or ‘long-necks’).

One example appears to be probably one of the fiercest group of marine predators: the mosasaurs (mosasauroid squamates; Madzia & Cau 2017). I will discuss this example in this post.

Fig. 1. The tree-based systematic groups of mosasaurs (Mosasauroidae plus ancient relatives) when applying Madzia & Cau's nomenclature to their Bayesian-inferred majority-rule consensus tree. Most higher taxa (above genus) are "branch-based", except for the "node-based" Mosasauridae, Russellosaurina (wrong suffix, kept as rank-less taxon by the authors), Tethysaurinae, and Yaguarasaurinae. Genera represented by a single OTU in blue, 'non-monophyletic' genera in red. Thick branches received near unambiguous support (PP ≥ 0.95)

Madzia & Cau “re-examined a data set that results from modifications assembled in the course of the last 20 years and performed multiple parsimony analyses and Bayesian tip-dating analysis” in order to identify the ‘weak spots’ and take them into account when providing a revised cladistic nomenclature of “the ‘traditionally’ recognized mosasauroid clades” (Fig. 1). They define possibly monophyletic groups via recurring branching patterns in their various trees, along with the position of key taxa in those trees (see their chapter Phylogenetic [in fact: cladistic] nomenclature). This allows the groups to “self-destruct” when not forming a clade, and to be replaced.

Although the combination of unweighted and differentially weighted parsimony and Bayesian tip-dating analyses could be methodologically interesting (when examined in detail), it is hardly necessary in order to identify weaknesses and strengths of the data matrix used – going back to Bell 1997, and being emended since (see Introduction of Madzia & Cau) – to define possible monophyletic (or other) groups. A quick and simple neighbour-net splits graph would have done the trick, too.

The situation regarding tree inference, e.g. parsimony

The mosasaurid data matrix suffers from the typical problems: ambiguous, highly homoplasious signals, paired with a few missing data issues (typically lack of data overlap). Adding to this is the miscellaneous signal from taxa regarded as outgroups (here: ancient potential members of the mosasaurs): Adriosaurus suessi (which the authors used to root their trees), Dolichosaurus longicollis, and Ponto-saurus kornhuberi. Accordingly, standard parsimony analysis fails to provide a useful result for about half of the taxa, when documented in the traditional fashion (see my last post) — a strict consensus cladogram of all most parsimonious trees (MPTs) is shown in Fig. 2A.

Fig. 2 Strict consensus graphs based on 152 equally (most) parsimonious trees inferred from the matrix (all characters treated as unweighted and unordered) using PAUP*. Green, unambiguous placement/grouping; turquois, weakly 'rogue-ish', red, rogue taxa

But even the Adams consensus tree (Fig. 2B) is more informative, and the (near) strict consensus network (only showing splits that occur in more than a single MPT) highlights where the equally parsimonious solutions agree and disagree, and which taxa act more ‘rogueish’ than others (Fig. 2C). Weighting and Bayesian inference naturally produce more resolved trees; but the question remains whether the overall higher to unambiguous branch support sufficiently reflects the signal in the character matrix.

Data sets of extinct organisms need neighbour-nets, to start with

The consensus network of the most (equally) parsimonious trees (MPT; Fig. 2C) informs us about equally valid topological alternatives and ‘rogueness’. Using the branch-length averaging option, we can visualize character support to some degree for the alternatives. But there is a quicker and more comprehensive alternative, when it comes to (tree-)incompatible signal.

The neighbour-net (Fig. 3) directly identifies potentially strong signals and ‘weak spots’. First, we can see that the outgroup taxa are not clustered, which is never good. Obviously, they are not too useful to infer an ingroup root (Madzia & Cau discuss the outgroup sampling bias). Only one of the outgrops, Pontosaurus, is placed closed to the Aigialosauridae, which collects the earliest diverging Mosasauroideae lineage (see Fig. 1). Their signals are likely to mess-up any tree inference (Fig. 2).

Fig. 3 The neighbour-net based on simple (Hamming) mean distances inferred from Madzia & Cau's matrix. Colouring as in Fig. 1

Trivial (data-wise) lineages are e.g. the Tylosaurinae, supported by a very long narrow branch— this lineage is characterised by high group coherence and distinctness to any other taxon/taxon group and will inevitably have high support and placed close (phylogenetically and absolute) to the Plioplate-carpinae (Figs 2, 3). The Mosasaurinae are equally well circumscribed, with only one putative member, Dallasaurus, being substantially apart from the rest, and bridging Mosasaurinae and Halisaurinae, their putative sisters. Hence, trees will favour splits rejecting the "Natantia" group unless Dallasaurus is excluded from the inference.

Species of the same genera are conspicuously grouped; this differs from Madzia & Cau’s trees, where Mosasaurus or Prognathodon species are collected in the same subtrees, but are “non-monophyletic”, i.e. do not form an exclusive clade. Based on the neighbour-net, the main reason may be terminal noise and resulting flat likelihood surfaces (hence, low posterior probabilities). The placement of the older members of the mosasaurs (classified as Tethysaurinae and Yaguarasaurinae) to each other, and the slightly older outgroup taxa, is clearly difficult with this matrix, even though there is no ambiguity, e.g. in the MPT sample (Fig. 2). Hence, the branch-lengths do not reflect synapomorphies or rarely shared apomorphies in this subtree, but instead shared convergences — a perfect phylogeny always generates a perfectly tree-like distance matrix.

Oddly placed taxa in the neighbour-net? Probably unrepresentative distances; and the quick fix

In contrast to trees, the network in Fig. 3 fails to resolve a likely position for one Prognathodon species: P. currii, and the large associated box indicates a data issue. The pairwise distances of the oddly placed P. currii and the probably misplaced Dolichosaurus, are poorly defined: both have zero-distances to non-similar taxa, but also to each other. But whereas Dolichosaurus differs from other members of Prognathodon by mean morphological distances (MD) of 0.5–1.0 (1.0 means it differs in all defined characters!), P. currii is much more similar to its congeners (MD = 0.17–0.27 and 0.46). Their other affinities also lie with strongly different taxon sets.

Their position in the neighbour-net is the result of a missing data artefact. Being just a 2-dimensional graph, such severe signal ambiguity cannot be resolved. Unrepresentative distances are the major (only) obstacle for neighbour-nets in the context of extinct groups. Trees are more decisive in such cases, when the few covered characters fit well the preferred tree's topology. By removing the outgroup taxa and P. currii, we can generate a neighbour-net (Fig. 4) in-line, and going beyond the Bayesian-tree-based groups suggested by Madzia & Cau (Fig. 1).

Fig. 4 Same data and method as shown in Fig. 3; four OTUs were excluded, the non-Mosasauroidea (outgroup) and the misplaced Prognathodon currii

Using networks to define taxonomic groups

Just based on the neighbour-nets (Figs 3, 4), circumscription of genera and higher taxa can be discussed (assuming that morphology mirrors phylogeny). For instance, Mosasaurus can be kept as-is or can include Plotosaurus; whereas the Clidastes form a clearly distinct taxon (whether paraphyletic/ monophyletic or clade/grade may be impossible to decide, see Fig. 1). Including (all) Prognathodon in the Globidensini remains an option; Eremiasaurus may be included, too, or included in the likely sister clade, the Mosasaurini.  

Dallasaurus is not only the oldest possible but clearly the most unique (primitive?) member of the Mosasaurinae, and the Halisaurinae likely represent their early diverged sister lineage. Treating Tylosaurinae and Plioplatecarpinae as reciprocally monophyletic sister lineages makes sense with respect to the older taxa and the co-eval Mosasaurinae-Halisaurinae lineage. The ancient forms are generally more similar to Plioplatecarpinae (+ Tylosaurinae) than to the Mosasaurinae and Halisaurinae lineages; but whether they should be included in the same systematic group ("Russellosaurina") cannot be judged based on the data matrix or the inferred trees (see also Figs 1, 2). Their topological attraction may be due to more shared primitive features (Hennig's ‘symplesiomorphies’), and the "Russellosaurina" could be a paraphyletic clade.

An interesting pronounced central edge bundle in the network in Fig. 4, which agrees well with Madzia & Cau's Bayesian consensus tree (Fig. 1), is the one separating all oldest, potentially more primitive taxa/lineages (> 90 Ma) from the later more diversified lineages (Mosasaurinae, Halisaurinae, Plioplatecarpinae, and Tylosaurinae). Regarding primitiveness vs. derivedness, an option to map characters on networks and extract alternative trees directly from the network would be handy (see also David’s 500^th post).

Fig. 5 Bootstrap (BS) support network based on 10,000 BS (pseudo)replicates optimised under parsimony. Splits are shown that occurred only in at least 20% of the BS replicates; trivial splits are collapsed. Some taxa have low, but unchallenged support, in other cases no preference at all is found (e.g. for the highest level bracketing taxa) or two alternatives compete with each other.

Also in the case of the mosasaurs: when we want to use phylogenetic trees as the sole (or main) basis for classification, rather than neighbour-nets (see my last post) and common sense backed up by EDA (e.g. Fig. 4; Bomfleur et al. 2017), the method of choice would be the support consensus networks based on parsimony (example provided in Fig. 5), least-squares, and/or likelihood bootstrapping pseudoreplicate samples. in addition to or instead of the Bayesian-inferred topologies sample. The posterior probabilities in Madzia & Cau’s tip-dated tree and Bayesian majority-rule consensus tree include values << 1.0, which already can be an indication of very strong signal conflict or just lack of discriminating signal (flat likelihood surfaces).

We should not be over-confident in PP, when the underlying data are not tree-like at all, as they too easily tilt towards one alternative (see also Zander 2004). The same holds for post-analysis character weighting, designed to eliminate (down-weigh) conflicting signals. While parsimony and distance methods are more easily affected by branching artefacts, probabilistic methods may struggle with flat likelihood surfaces. Thus, bootstrap support networks should be the first choice for ‘phylogenetic’ (by identifying Hennigian monophyla) or ‘cladistic’ (clade-based) classification as they show the robustness of the signal for the preferred and other topological alternatives, and can be generated under different optimality criteria. Having a certain support for a clade is nice, but one should always consider the support for alternatives, and consider how many characters support or oppose an alternative.

Morphological matrices need to be analysed using network approaches

Madzia & Cau’s study is methodologically interesting by providing a tip-dated Bayesian tree for an extinct group of organisms. A one-to-one comparison of their parsimony-BS support using different character and weighting schemes vs. Bayesian PP may be interesting, too — note the difference between the tip-dated tree and the majority rule consensus trees for several critical branches. However, following the current standard practice, no BS pseudoreplicate and Bayesian saved topologies samples were provided. Regarding the main objective, the identification of ‘weak spots’ to propose enhanced systematic groups, networks (Figs 2–5) would have been more informative and straightforward.

No matter what classification philosophy is applied, when we deal with morphological matrices of extinct groups of organisms, the first step should always be to explore the primary signal in the data before we infer trees using (highly) sophisticated methods, and interpret them — the latter may actually obscure ‘weak spots’ rather than identifying them. The quickest analyses are neighbour-nets, but watch out for odd pairwise distance patterns (easily visualised using heat maps)!

The second step is producing support consensus networks, for the fine-tuning and to decide on the most probable trees to explain the data. Regarding classification, we should ask ourselves whether we really want inevitably unstable clade-based classification systems (when dealing with extinct organisms), or robust ones that reflect the general data situation and include potentially or likely paraphyletic taxa (see e.g. Clidastes in Figs 2–5 and Madzia & Cau's trees, and their elaborate discussion of higher level taxa, which – to a good degree – could become superfluous when allowing paraphyletic taxa).

Links

All graphics, and some primary data files, are publicly available from figshare. An archive including all re-analysis files can be downloaded at www.palaeogrimm.org.

References

Bell GL (1997) A phylogenetic revision of North American and Adriatic Mosasauroidea. In: Callaway JM, and Nicholls EL, eds. Ancient Marine Reptiles. San Diego: Academic Press, pp. 293–332 [cited from Madzia & Cau 2017]

Bomfleur B, Grimm GW, McLoughlin S. 2017. The fossil Osmundales (Royal Ferns)—a phylogenetic network analysis, revised taxonomy, and evolutionary classification of anatomically preserved trunks and rhizomes. PeerJ 5:e3433. https://peerj.com/articles/3433/.

Madzia D, Cau A (2017) Inferring 'weak spots' in phylogenetic trees: application to mosasauroid nomenclature. PeerJ 5: e3782. https://peerj.com/articles/3782/.

Zander RH (2004) Minimal values of reliability of Bootstrap and Jackknife proportions, Decay index, and Bayesian posterior probability. PhyloInformatics 2: 1–13.

Are taxonomies networks?

One of the basic tenets of modern systematics is that taxonomies should be hierarchical. That is, we arrange things in a nested hierarchy, with decreasing similarity among the objects as we proceed towards the tip. Indeed, one of Darwin's arguments for his version of biological evolution was that specie splitting leads naturally to a hierarchical taxonomy.

However, it is clear that not everyone agrees with this idea. The web is full of things labelled "taxonomy" but which are clearly networks. I have gathered a few of them here for you.

The first example is from Business Insider UK, Everything you need to know about beer, in one chart. It seems to be quite informative.

An even more complex version, and thus much more network-like, is available at Pop Chart Lab: The magnificent multitude of beer. However, this is not labelled as a "taxonomy". Just as an aside, there is also A periodic table beer styles (an earlier version is here).

The next one is ubiquitous on the web, but appears to come from Charley Chartwell: A grand taxonomy of Shakespearean insults. It may give you some good ideas!

The next one also comes from Pop Chart Lab: The grand taxonomy of rap names.

Here is a version without the centre obscured, although it is no longer labelled as a taxonomy:

Next we have one from Stephen Wildish: The fish & chip taxonomy.

This final network is a bit more cheeky than the others. It is also from Stephen Wildish: A taxonomy of arse.

There are many other "taxonomies" out there, many of which are basically star trees, with very few being truly tree-like. Here is a simple "tree" taxonomy, which comes from Kate Turner: The taxonomy of my music. Unfortunately, I think that in reality it should probably be a network, like the others.

Phylogenetics of computer viruses?

There is a difference between phylogenetics and clustering or classification. The latter processes put objects into groups based on some intrinsic features, but the former uses their intrinsic features to expresses their evolutionary history. Not all objects have an evolutionary history, even though they can all be put into groups. Furthermore, even objects that do have a history do not necessarily have an evolutionary history. Evolution involves ancestor-descendant relationships (as well as sister-group relationships), and not all of history involves ancestors and descendants.

This distinction is important for the use of phylogenetics as a metaphor for the history of non-biological objects. Outside of biology, many things are claimed to have a "phylogenetic history", including languages and most human artifacts. As I have noted before, one has to be careful when applying this metaphor (see False analogies between anthropology and biology).

One particular example that I have encountered involves the development of computer viruses and other malware (Iliopoulos et al. 2008). Metaphorically, such viruses can be seen to be phylogenetically related, because new viruses are often based on previous ones — that is, one virus "begets" another virus due to changes in its intrinsic attributes. In this sense the metaphor is helpful, although there is no actual copying of anything resembling a genome — this is phenotype evolution not genotype evolution.

Sorkin (1994) seems to have been the first to discuss the possibility of computer virus evolution, but the first empirical attempt to reconstruct a digital phylogeny appears to have been by Hull (1995b), who studied the Stoned computer virus (a virus that infected the boot sector of PCs between 1990 and 1995), as shown below.

Since then, phylogenetics has been a popular topic in the study of computer malware (eg. Goldberg et al. 1996; Carrera & Erdélyi 2004; Karim et al. 2005a,b; Ma et al. 2006; Wehner 2007; Walenstein et al. 2007; Wagener et al. 2008: Hayes et al. 2009; Khoo & Lió 2011; Guan et al. 2012). As noted by Webster & Malcolm (2007) these studies "present classifications of malware based on phylogenetic trees, in which the lineage of computer viruses can be traced and a 'family tree' of viruses constructed based on similar behaviors." (Note that there are other possible uses of phylogenetics related to computer programming, as exemplified by Ji et al. 2008.)

In all cases the phylogeny was produced using a distance-based clustering algorithm (ie. the tree is a phenetic one). Some of the distances are well motivated in terms of historical changes in the intrinsic attributes of the malware, but that does not necessarily make the resulting phenogram a phylogeny. So, the methods use basic clustering techniques to produce a tree, thus treating classification as phylogenetics (or phenetics as phylogenetics). This certainly clusters the objects, but there is no necessary reason for the clustering to reflect phylogeny.

Thus, a simple concept of clustering is inadequate, even though it can be used to construct a tree. A phylogenetic tree expresses the nested hierarchy formed by the shared derived character states, but not by anything else. A tree expresses nested clusters, but it is a form of "special nesting" that expresses a phylogeny. Only one form of tree is relevant to phylogenetics, and trees formed in other ways are likely to be suitable only under the simplest circumstances.

Furthermore, the general conception in these papers of a virus phylogeny as tree-like is clear. As noted by Hull (1995a):

Computer viruses evolve in complex ways not usually encountered in nature. The transplantation of large segments of computer code from one virus to another need not represent evolutionary relationship, for example. A newer virus may just represent a debugged or patched earlier version. The virus author may have deliberately incorporated parts of other viruses as a short cut, or because the plagiarized code is useful. If the virus incorporates code generating 'engines', similar code may appear in viruses with no other similarities. Structural similarities deriving from functional similarities likewise derive from several sources.

As we now know, these sorts of evolutionary events are usually found in nature, but they create reticulate histories, involving horizontal as well as vertical evolution. That is, computer virus phylogenetics involves reticulation — new computer code takes bits and pieces from various previous viruses. In particular, there is also what is called "oblique" evolution, in which there is horizontal evolution between generations. This is a characteristic of many histories involving human artifacts (see Time inconsistency in evolutionary networks), and it allows information to "time travel", so that the information available for horizontal transmission can come from the distant past as well as from the present.

So, malware evolution is not tree-like. Only two of the papers cited above seem to acknowledge this fact. Khoo & Lió (2011) were quite conventional in using splits graphs rather than unrooted trees to display their data, although they do not specify the algorithm for producing the networks. They do, however, claim that "networks were more useful for visualising short nop-equivalent code metamorphism than trees".

Goldberg et al. (1996) were more innovative, and analyzed their data using what they called a "phyloDAG", which is a directed network that can have multiple roots (it appears to be a type of minimum-spanning network). Interestingly, they note that "Beyond the computer virus realm for which it was conceived, the phyloDAG is also a plausible model for evolution of bacterial populations." Indeed, the possibility of multiple roots has been explicitly suggested for prokaryote phylogenetics (see Can networks have multiple roots?). I wouldn't doubt that it is also feasible for language history.

References

Carrera E, Erdélyi G (2004) Digital genome mapping – advanced binary malware analysis. Virus Bulletin Conference 2004.

Goldberg LA, Goldberg PW, Phillips CA, Sorkin GB (1996) Constructing computer virus phylogenies. Lecture Notes in Computer Science 1075: 253-270. [also Journal of Algorithms (1998) 26: 188-208]

Guan Q, Tang Y, Liu X (2012) A malware homologous analysis method based on sequence of system function. Advanced Science and Technology Letters, ASTL 15: Advanced Computer Science and Technology. Science and Engineering Research Support Society, Sandy Bay, Tasmania, Australia.

Hayes M, Walenstein A, Lakhotia A (2009) Evaluation of malware phylogeny modelling systems using automated variant generation. Journal in Computer Virology 5: 335-343.

Hull DB (1995a) Computer viruses: naming and classification. Virus Bulletin Sept: 15-17.

Hull DB (1995b) Computer viruses: naming and classification, part II. Virus Bulletin Oct: 16-17.

Iliopoulos D, Adami C, Ször P (2008) Darwin inside the machines: malware evolution and the consequences for computer security. Virus Bulletin Conference 2008.

Ji J-H, Park S-H, Woo G, Cho H-G (2008) Generating pylogenetic tree of homogeneous source code in a plagiarism detection system. International Journal of Control, Automation, and Systems 6: 809-817.

Karim ME, Walenstein A, Lakhotia A (2005a) Malware phylogeny using maximal pi-patterns. Proceedings of the EICAR 2005 Conference, pp 156-174.

Karim ME, Walenstein A, Lakhotia A, Parida L (2005b) Malware phylogeny generation using permutations of code. Journal in Computer Virology 1: 13-23.

Khoo WM, Lió P (2011) Unity in diversity: phylogenetic-inspired techniques for reverse engineering and detection of malware families. Proceedings of the 2011 First Systems Security Workshop (SysSec'11), pp 3-10. IEEE Computer Society Washington, DC.

Ma J, Dunagan J, Wang HJ, Savage S, Voelker GM (2006) Finding diversity in remote code injection exploits. Proceedings of the 6th ACM SIGCOMM Conference on Internet Measurement, pp 53-64. ACM, New York.

Sorkin GB (1994) Grouping related computer viruses into families. Proceedings of the IBM Security ITS 1994.

Wagener G, State R, Dulaunoy A (2008) Malware behaviour analysis. Journal in Computer Virology 4: 279–287.

Walenstein A, Hayes M, Lakhotia A (2007) Phylogenetic comparisons of malware. Virus Bulletin Conference 2007.

Webster M, Malcolm G (2007) Classification of computer viruses using the theory of affordances. Second International Workshop on the Theory of Computer Viruses.

Wehner S (2007) Analyzing worms and network traffic using compression. Journal of Computer Security 15: 303-320. (arXiv:cs/0504045v1, 2007)

The phylogenetics of angiosperm classification schemes

Alain Cuerrier, Luc Brouillet and Denis Barabe (1998. Numerical and comparative analyses of the modern systems of classification of the flowering plants. Botanical Review 64: 323-355) have provided a genealogy of the various classifications that have been produced for the angiosperms (flowering plants). This is a theoretical construction, intended to express the lines of intellectual influence, either directly expressed by the authors of the classifications, or inferred by comparison of the classifications themselves.

As shown here, it is a classic directed acyclic graph, most of which is tree-like, although some parts are distinctly bushy. Of interest to us, there are also places where hybridizations are indicated.

Cuerrier et al. analyzed the structure of the four modern classifications (by Cronsquist, Dahlgren, Takhtajan, and Thorne) in comparison to their immediate predecessors (by Bessey, Engler, Hallier, and also Gobi). This was a study of affinity relationships, rather than genealogy, and one of their study questions was whether the affinity relationships matched the genealogical ones.

In this regard it is interesting to note that they used clustering and ordination techniques to analyze their quantitative data (comparing the classifications), but they did not use any network techniques. Yet, this would seem to be an obvious strategy, given that they were expecting reticulating relationships.

Unfortunately, none of the datasets shown in the paper is complete, and so I cannot provide a network analysis for them.

The authors summarized their suite of multivariate analyses as an interaction network, as shown next. For each pair of classifications, four statistical tests were performed, and the thickness of the arrows in the network indicates the degree of significant similarity detected: dotted arrow = 2/4 tests show similarity, thin arrow = 3/4 tests, and thick arrow = 4/4 tests.

These semi-quantitative relationships can also be expressed as an unrooted phylogenetic network. I simply took the pairwise similarity scores (0.0, 0.25, 0.5, 0.75, 1.0) and analyzed them using a NeighborNet network. The four modern classifications are highlighted in red.

This more clearly illustrates the various points made by Cuerrier et al. In particular, they note that the intellectual genealogy is not reflected in the affinity relationships of the modern classifications. For example, the Cronquist and Takhtajan classifications are much more similar to that of Hallier than to that of Bessey, whereas Cronquist explicitly cites Bessey as a major influence on his work. Instead, Cronquist's classification is more similar to that of Engler, who does not appear to be genealogically related at all. The distinction between the Thorne and Dahlgren classifications and those of Takhtajan and Cronquist is also obvious.